Q. No.Three resistors having resistances \(r_1, r_2~\text{and}~r_3\) are connected as shown in the given circuit. The ratio \(\dfrac{i_3}{i_1}\) of currents in terms of resistances used in the circuit is:
1. \(\dfrac{r_1}{r_1+r_2}\)
2. \(\dfrac{r_2}{r_1+r_3}\)
3. \(\dfrac{r_1}{r_2+r_3}\)
4. \(\dfrac{r_2}{r_2+r_3}\)
The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section, and same material is \(0.25~\Omega\). What will be the effective resistance if they are connected in series?
1. \(1~\Omega\)
2. \(4~\Omega\)
3. \(0.25~\Omega\)
4. \(0.5~\Omega\)
In a potentiometer circuit, a cell of emf \(1.5~\text{V}\) gives a balance point at 36 cm length of wire. If another cell of emf 2.5 V replaces the first cell, then at what length of the wire, the balance point occur?
1. 64 cm
2. 62 cm
3. 60 cm
4. 21.6 cm
Match Column-I and Column-II with appropriate relations.
| Column-I | Column-II | ||
| \(\mathrm{(A)}\) | Drift Velocity | \(\mathrm{(P)}\) | \(\dfrac{{m}}{{ne}^2 \rho}\) |
| \(\mathrm{(B)}\) | Electrical Resistivity | \(\mathrm{(Q)}\) | \(nev_d\) |
| \(\mathrm{(C)}\) | Relaxation Period | \(\mathrm{(R)}\) | \(\dfrac{ {eE}}{{m}} \tau\) |
| \(\mathrm{(D)}\) | Current Density | \(\mathrm{(S)}\) | \(\dfrac{E}{J}\) |
| \(\mathrm{(A)}\) | \(\mathrm{(B)}\) | \(\mathrm{(C)}\) | \(\mathrm{(D)}\) | |
| 1. | \(\mathrm{(R)}\) | \(\mathrm{(P)}\) | \(\mathrm{(S)}\) | \(\mathrm{(Q)}\) |
| 2. | \(\mathrm{(R)}\) | \(\mathrm{(Q)}\) | \(\mathrm{(S)}\) | \(\mathrm{(P)}\) |
| 3. | \(\mathrm{(R)}\) | \(\mathrm{(S)}\) | \(\mathrm{(P)}\) | \(\mathrm{(Q)}\) |
| 4. | \(\mathrm{(R)}\) | \(\mathrm{(S)}\) | \(\mathrm{(Q)}\) | \(\mathrm{(P)}\) |
The equivalent resistance between \(A\) and \(B\) for the mesh shown in the figure is:
| 1. | \(7.2~\Omega\) | 2. | \(16~\Omega\) |
| 3. | \(30~\Omega\) | 4. | \(4.8~\Omega\) |
For the circuit given below, Kirchhoff's loop rule for the loop \(BCDEB\) is given by the equation:
| 1. | \(-{i}_2 {R}_2+{E}_2-{E}_3+{i}_3{R}_1=0\) |
| 2. | \({i}_2{R}_2+{E}_2-{E}_3-{i}_3 {R}_1=0\) |
| 3. | \({i}_2 {R}_2+{E}_2+{E}_3+{i}_3 {R}_1=0\) |
| 4. | \(-{i}_2 {R}_2+{E}_2+{E}_3+{i}_3{R}_1=0\) |
Two solid conductors are made up of the same material and have the same length and the same resistance. One of them has a circular cross-section of area \( 𝐴 _1\) and the other one has a square cross-section of area \(A_2.\) The ratio of \(𝐴 _1 / 𝐴 _2 \) is:
1. \(1.5\)
2. \(1\)
3. \(0.8\)
4. \(2\)
For the circuit shown in the figure, the current \(I\) will be:
| 1. | \(0.75~\text{A}\) | 2. | \(1~\text{A}\) |
| 3. | \(1.5~\text{A}\) | 4. | \(0.5~\text{A}\) |
| 1. | \(4:1\) | 2. | \(1:2\) |
| 3. | \(2:1\) | 4. | \(1:4\) |
1. \(10^{5}\) A/m2
2. \(10^{4}\) A/m2
3. \(10^{6}\) A/m2
4. \(10^{-5}\) A/m2
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